Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

Abstract

The interactions between vortex tubes and magnetic-flux rings in incompressible MHD are inves- [MHD]), and, via its convection by the velocity field, becomes turbulent, developing coherent structures of its own. Thus, it is conceptually important to understand the interactions between structures in the gauge and inertial fields, and the way these can help understand (in a structural way) some of the complexity of turbulent chaos, (b) the presence of the Lorentz force in the Navier-Stokes equations enables the depiction of wave phenomena in the latter (Alfven waves), which lead to novel (in comparison with incompressible turbulence)

Helicity spectra and topological dynamics of vortex links at high Reynolds numbers

“…It would be interesting, for example, to investigate the topological and helicity dynamics of magnetohydrodynamic vortex links. Such studies would significantly expand previous vortex-dynamical magnetohydrodynamic investigations (Kivotides 2018a(Kivotides , 2019. Another important problem is the topological and helicity dynamics of vortex knots, and possible connections between topology and energy and helicity spectra there, in conjunction with advanced topological measures including knot polynomials (Liu & Ricca 2015;Cooper et al 2019) and Vassiliev invariants.…”

Magnetic knot cascade via the stepwise reconnection of helical flux tubes

“…We set ν = η = 0.005, with the magnetic Prandtl number Pr ≡ ν/η = 1. In this case, the magnetic field has a strong action on the fluid flow, characterized by a large interaction parameter N i = b 2 0 r c /(ηu 0 ) = 2.26 × 10 3 (see Davidson 2001;Kivotides 2018).…”

“…The observations in figures 4, 7 and 13 imply that the major mechanism for the current magnetic reconnection is the X-type reconnection (see Priest & Forbes 2000;Pontin 2011), which is similar to viscous cancellation rather than bridging (see Melander & Hussain 1988;Kida & Takaoka 1994) in vortex reconnection. It is noted that vortex lines can be tangled under the strong self-induced local velocity generated in the incipient reconnection of vortex lines, whereas the reconnection of field lines can only alter the local velocity via an implicit way at moderate and large interaction parameters (see Kivotides 2018).…”

Superfluid helium-4 hydrodynamics with discrete topological defects

“…In order to calibrate the new model, we compare its predictions with a standard computation of a superfluid vortex ring propagating in a quiescent normal-fluid [28]. The numerical methods employed in the calculation are described in [15,29,30], which should be consulted…”

“…The superfluid ring radius is R = 0.25l b , and its initial position is on the centre of the box. On top of the truncation errors of the numerical analysis (as discussed in[15,29,30]), the algorithmic calculations introduce round-off errors, since they employ finite precision arithmetic[31] within the set of floating point numbers F −1022,1023 2,53 , where 2 indicates binary arithmetic, and 53 the precision (significant binary digits). Hence, the distance between 1 and the next larger floating point number is ǫ m = 0.222 × 10 −15 .…”